- Email: [email protected]
Instrument for the automatic measurement of the electrode admittance
ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., L a u s a n n e - P r i n t e d in T h e N e t h e r l a n d s
181
I N S T R U M E N T FOR T H E AUTOMATIC MEASUREMENT OF T H E E L E C T R O D E ADMITTANCE*
R. D E L E V I E AND A. A. H U S O V S K Y
Department of Chemistry, Georgetown University, Washington, D. C. 2ooo7 (U.S.A.) (Received A u g u s t 8th, 1968)
INTRODUCTION
The measurement of the electrode admittance is fundamental to modern electrochemistry. On the basis of the Lippmann equation 1, GouY 2 accurately predicted the double-layer capacitance of aqueous solutions like o. 5 M Na~S04 and o.5 M H2S04 from surface tension measurements of unparalleled precision. The direct measurement of the electrode admittance became possible only after PROSKURNIN AND FRUMKIN3 had demonstrated the effect of organic impurities on the capacitance of stationary electrodes, and after GRAHAME4 had developed instrumentation to circumvent this problem b y using a dropping mercury electrode. Since then, bridge measurements of the electrode admittance have been used extensively, and have contributed significantly to our understanding of the double-layer structure 5, the kinetics of electrode reactions 6 and adsorption processes 7, and, recently, of the interplay between adsorption and electrode kinetics s. All these developments were based on bridge measurements like those of GRAHAME a, which are precise but time-eonsmning. Many attempts have been made to obtain the same information more rapidly. So-called a.c. polarography was developed b y MACALEAVY9 and BREYER AND GUTMANN 10, but it neglected the effects of resistance in series with the electrode and the phase relationship between voltage and current. Modern instrumentation goes back to two patents of JESSOP, who introduced phase-sensitive detection 11 and automatic compensation for series resistance v i a positive feedback 12. An instrument incorporating these innovations 13 has found a rather limited acceptance for general electrochemical work as it was designed primarily for analytical use. Only recently have JESSOP'S ideas been incorporated in other instruments. DEFORD et al. 14 described an instrument which monitors the absolute magnitude and the in-phase component of the electrode admittance, using both positive feedback and phase-sensitive rectification. A different approach is that of HAYES AND R E I L L E Y 15, who described an instrument which elegantly avoids the difficulties of positive feedback and uses a multiplier for phaseselective detector. In the present communication, we will describe an instrument similar to that of DEFORD et al. 14 with the incorporation of modern lock-in techniques. This instrument has been in continuous use for well over a year without major * T h i s m a n u s c r i p t is s u b m i t t e d for p u b l i c a t i o n w i t h t h e u n d e r s t a n d i n g t h a t t h e U n i t e d S t a t e s G o v e r n m e n t is a u t h o r i z e d to r e p r o d u c e a n d d i s t r i b u t e r e p r i n t s for g o v e r n m e n t a l p u r p o s e s .
j . Electroanal. Chem., 20 (1969) 181-193
182
R. DE LEVlE, A. A. HUSOVSKY
breakdown, and has been applied to a number of problems ranging from measurements of double-layer capacitance and faradaic impedance to those of photo-emission of electrons. It is specifically designed for use with a dropping mercury electrode. CIRCUIT DESCRIPTION
An alternating voltage is derived via follower i and a divider network from an external oscillator, and is fed to the summing point (negative input) of a potentiostatbooster combination, 3 + 4, see Fig. I. Also fed to that summing point are an initial potential derived from the power supply via a potentiometer, a voltage ramp from integrator 2, the output of follower 5 sensing the potential of a reference electrode (the usual negative feedback loop) and a fraction of the output of current amplifier, 6. The latter signal provides the positive feedbackS2,14,16 correcting for resistance between the reference electrode and the negative input of amplifier 6. The output of amplifier 6 is passed through a second order high-pass filter 7, further amplified (8) and inverted (9)- The outputs of 8 and 9 are chopped by FET series switches, summed by amplifier IO and finally averaged by a third-order low-pass Butterworth filter i i . The signal driving the FET choppers is derived from the a.c. input after phase-shifting (i2), squaring, proportioning (13) and inverting (14). Thus,
INITIAL
OJ-EO0 SENSITIVWY OSCILLATOR IN ~"
AC AMPLITUDE
GAIN IO-IOOO
POSITIVE FEEDBACK
IOO
reference HIGH PASS FILTER
-isv ~ 5
O.I nF
zoo:.>
-
v leo
,'~1-I J t nF-I/,LF
/-/m
2c
LOW PASS FILTER
WAVE SQUARER
PHASE SHIFTER
Fig. i. The electronic circuit used. Amplifiers i - 6 control the voltage, ~nd ~mp. 7 - I 4 m e a s u r e t h e c u r r e n t via s y n c h r o n o u s rectification. Amp. 2: Philbrick SP 2 A U ; amp, 4: B u r r B r o w n 3oi6/25; a m p . 6: Philbrick P 45 AU; all other a m p . : Philbrick P 65 A H U . Resistors: Sprague metal film t y p e 420 EBC 3, values in k ~ (except for I G~2 in r a m p generator circuit); t r a n s i s t o r s : M P F lO 5. Resistor box in positive feedback loop: General Radio 1434 G. The c o m p e n s a t e d resistance is given b y R R ' / I O ( R + 5 ) for R 4 1 o o , where R" is the value of the feedback resistor across amp. 6 (sensitivity) and R the value dialed on the positive feedback resistor box, all values t a k e n in k ~ . Only one of two identical phase-shifting RC n e t w o r k s is s h o w n on the positive i n p u t of a m p . I 2 ,
J. EIectroanal. Cl~em., 20 (1969) 181-193
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
183
amplifiers 7-I4 comprise a simple lock-in amplifier~t, 17 and may be replaced by a commercial unit. The following switches were omitted from Fig. I for greater clarity: a resethold-scan switch on the ramp generator 2, a switch connecting the positive input of follower 5 directly to the output of booster 4 (for use with 2 electrodes and dummy cells), a switch replacing the cell by a d u m m y consisting of a resistor in series with either .~G. PASS F,LTER 0__~.1
4
0.1
0.1
Low PASS F,-TEF~
4
0.[
200
400 ZOO 400 400
4-15V 20
5.6
5.6 1.5
IN ~
OUT
I 15
2N 4123
WAVE SQUARER
Fig. 2. T h e (second-order) h i g h - p a s s filter, (third-order) low-pass filter a n d w a v e - s q u a r e r of Fig. I. Amplifiers: P h i l b r i c k P 65 A H U . R e s i s t a n c e in kf2, c a p a c i t a n c e in # F . H5 VO¢
-15V
IN 2 0 7 t 6
54 A C .
865C
'41
)
2N 525
30tzg
2
1,651
/ **.sv 5,1
62<~
T-,sv 680pF 680 pE 5.1
4.7IF
ALLIED
120
~¢ISV
Fig. 3. Circuit d r i v i n g t h e h a m m e r coil (Guardian) a n d a double-pole d o u b l e - t h r o w r e l a y (Allied) w h i c h switches one p h a s e - s h i f t i n g R C c o m b i n a t i o n on a m p . 12 for a n o t h e r , t h u s yielding altern a t e l y i n - p h a s e a n d q u a d r a t u r e readings. C o n n e c t i n g p o i n t a or b to g r o u n d via 22 k ~ will fix t h e position of t h e r e l a y so t h a t o n l y one v e c t o r c o m p o n e n t is registered, as in Fig. 4. R e s i s t a n c e in kf~.
j . Electroanal. Chem., 2o[(1969) 181-193
I84
R. DE LEVIE, A. A. HUSOVSKY
another resistor or a capacitor (for phase adjustment and calibration), and finally a relay-driven switch replacing one adjustable resistor-capacitor combination by another, similar one in the phase-shifting network of amplifier 12. Details of the filters and of the wave squarer (a simple Schmidt trigger) are given in Fig. 2. The potentiometers for initial potential and ramp speed can be connected to + I5V , ground, or - I 5 V on the Philbrick PR3oo power supply used. Separate + I5V and - I 5 V wires lead from the power supply to each amplifier. Right at the amplifier sockets, I5-/,F electrolytic capacitors are connected between ground and the power supply terminals in order to prevent high-frequency signal transmission via the power supply. The ground bus is made out of 1/8 in. o.d. copper tubing, with connections kept as short as possible. Oscillator used: General Radio I3IoA; XY recorder: Hewiett Packard 7035 BM. Figure 3 illustrates the switching mechanism which regulates the drop-time. A synchronous motor drives a cam which actuates two microswitches, MI and M2. Closing of MI deactivates the electrical pen lift on the recorder, so that a data point is plotted. Closing of ~ 2 drives a hammer which dislodges a mercury droplet f ore the electrode, and also replaces one phase-shifting network (Fig. I, amplifier 12) by the other. Thus, alternate readings can yield the in-phase and quadrature components of the electrode admittance. A manual switch-setting overrides the alternation of phase-shifting networks in case only one component is wanted. INSTRUMENT PERFORMANCE
Measurements on a dummy cell (o.I-I/~F in series with o . i - i o o k~) indicated that adequate correction for uncompensated resistance up to about io k ~ can be achieved at frequencies up to about i kHz. At higher frequencies, phase shifts in the feedback loop prevent proper compensation. Reduction of the feedback capacitor across the potentiostat amplifier (3 in Fig. I) raises the frequency limit, but invariably leads to uncontrollable oscillations when the dummy is replaced by an actual electrochemical cell. Other feedback configurations 16 and other amplifiers have been tried, but the performance seems to be roughly the same. Apparently, stray capacitance and inductance in tile instrument, the cell and the cell leads, limits the frequency response. The lower frequency limit of the instrument is determined by the Butterworth filters used, The filters of Fig. 2 have 3 db. points of about 16 Hz. Operation at somewhat lower frequencies using other filters, is quite feasible as long as the frequency used significantly exceeds those associated with drop growth is and as long as the low-pass output filter does not introduce a measurable time-lag which would lead to a ~'esponse which is too low, especially when the instrument is calibrated with a dummy cell. This latter point is not always appreciated 19, A fair idea of the performance of the instrument can be obtained from the following examples. Figure 4 shows actual measurements (every single mercury droplet yields one single point) of the double-layer capacitance of o.I M KC1 at 200 Hz. Comparison with data obtained by GRA!4AME ~°, Fig. 5, shows agreement to within the readability of tile recorder data. Figure 6 shows the in-phase and quadrature components of the electrode impedance of a solution of hexamethylphosphoramide. Note that the desad* peaks exhibit both in-phase and quadrature components at this * desorption-adsorption
j . Electroanal. Chem., 20 (1969) 181-193
I85
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
h
0.8
-..
3
8
~ 0.6
.+2_
E ~ 0.4
2 El
I
0,2
02
I
0.4
£~.6 0.8 -E(V vs. intePnal Ag/AgCI)
I
1!0
1.2
Fig. 4. Q u a d r a t u r e c o m p o n e n t of the electrode a d m i t t a n c e for o. i M KC1 at 25 o. Alternating voltage : 2o0 Hz, amplitude io m V (20 mV top-to-top). Compensated resistance: 322~. E v e r y single p o i n t corresponds to one m e r c u r y droplet. D r o p - t i m e regulated at 6.o0 sec. B o t t o m curve shifted b y o,8 V, covering range, - - i . o to --1.8 V. An independent, duplicate r u n does n o t differ b y more t h a n o. 5 m m in a d m i t t a n c e over the whole range of potentials; o. 5 m m corresponds to o. 15 # F cm-2. This suggests t h a t the m a i n source of error is the readability of the recorder trace. A digital voltmeter, gated b y the pen-lowering signal, m i g h t be used to c i r c u m v e n t this difficulty if higher readability is required. I n s t r u m e n t sensitivity w a s calibrated w i t h capacitors of accurately k n o w n capacitance, hence the a d m i t t a n c e axis is indicated in t e r m s of microfarads. The p r o p e r u n i t of admittance, ~ t, is obtained b y multiplication of the capacitance, in farads, b y the a n g u l a r frequency ~o of the sine w a v e used. This explains the use of, e.g., 318 Hz (o~ ~ 2000 t a d sec -1) in Fig. 6. 4O
30
~7 v
2O
~s
1 0.2
I o,4
I
I 0.6
I
I o.e
I
t
I
I,o
-E(Vvs. Tnterna/ Ag/Ag Cl)
Fig. 5. Comparison of double-layer capacitance d a t a calcd, from Fig. 4 (points) and bridge m e a s u r e m e n t s of GRAHAME20 (line). Note the e x p a n d e d capacitance scale. F o r the calculation, the following measured d a t a were used: m e r c u r y mass flow rate 0.635--0.007 mg sec 1, drop age 5.867±O.OLO sec, corresponding to a spherical drop of 2.045 ~ o . o I 5 ram2 surface area. The potential scale used is 37 m V negative with respect to o.i NCE, 16 m V more positive t h a n NCE.
j . Electroanal. Chem., 20 (1969) 181-193
186
R. DE LEVIE, A. A. HUSOVSKY
frequency, in agreement with theory ~1. Figure 7 illustrates the redox* peak of indium(III) in thiocyanate, and the negative Faradaic admittance22, 23 in the region of the polarographic minimum, Fig. 8. Bridge measurements in the latter region are often hampered by oscillations 24 resulting from the interplay of tile negative admittance and the inductance of bridge transformers. Figure 9 shows the highly irreversible reduction of hexaquonickel(II) and the more reversible reduction of a basic nickel polymer. The latter is not obvious from the d.c. polarogram (Fig. Io) in view of its
°'7t .." 0.6
."'
-
::
•
~o.41 ~
. '.
O.
"
-~ o.2~ 0.1
"
: ..
0
"-
0.2
" . . . . . . . . . . .
.=
........~....................J..................!...................!...................~..; ,,....!................!....._......~ 0,4
0.6
0.8
1.0
L2
1.4
1.6
1-8
- E ( V VS. S C E )
Fig. 6. Q u a d r a t u r e (top) and in-phase (bottom) c o m p o n e n t s of the electrode a d m i t t a n c e of o.I M N a F satd. w i t h N20 a n d containing o.1% (v]v) of h e x a m e t h y l p h o s p h o r a m i d e , OP(N(CH3)2)a. Alternating voltage: 318 Hz, amplitude io inV. Compensated resistance: 616 ~ . Note the inp h a s e c o m p o n e n t s of the desad peaks,
low concentration (about o.1% of the total nickel concentration). Finally, Fig. i i shows how this type of instrumentation can be used to measure electrochemical photocurrents. In this case, the wave generator is omitted, and the mercury drop illuminated with monochromatic light, obtained in our set-up from a Ioo-W mercury lamp (PEK IiO) with quartz collimator lense, interference filter, two choppers and focusing lenses. One chopper interrupts the light beam at a frequency in the range, 15-Iooo Hz, with a separate photo-detector providing the reference signal for the synchronous rectification. The second chopper rotates at o. i Hz, alternately passing and interrupting the light beam for periods of 5 sec. It also actuates the microswitches regulating the pen lift and drop hammer. Consequently, alternate points indicate photo-current and dark current, see Fig. 12. The above data are presented for the purpose of illustration only. We will elaborate on the electrochemical aspects of some of the above systems in another publication. DISCUSSION
A.c. polarography without correction for uncompensated resistance is restricted to low frequencies, low solution resistivity and low concentrations of electroreducible substances, for the effects of uncompensated (solution and capillary) resistance to be * reduction-oxidation
f . Electroanal. Chem., 2o (1969) 181-193
z87
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
..." .."
0.5 i... ................................ ,-:
.:.'"-....
..
•
.
..
..
j
""....
electrode 0.4 - a d m i t t a n c e (~F)
.,
, .. j-":
O~
quadrature
0.2 ~
.
component
0,1 - -
..
,., ..:"
J..................................... .:' o
1
1
0.1
0. 9
I 0.3
I................. 1..... I 0.4 0.5 ",.0.6
I O~
I 0.8
I 0.9
-0.1
:, .-
-0.2
.:'1
.'" 1.0
I I.I
I 1.2
I 1.4
I 1.3
I 1.5
- E (V vs. internal Ag/AgSCN)
." in-phase : component
-0.3
-0~"
-0.5
"......
Fig. 7. I n - p h a s e a n d q u a d r a t u r e c o m p o n e n t s of t h e electrode a d m i t t a n c e of 2 m M In(SCN)3 in I.O M N a S C N acidified w i t h H S C N to p H 3.24 a t 25 °. A l t e r n a t i n g voltage: 31.8 Hz, a m p l i t u d e io mV. C o m p e n s a t e d resistance: 2o6 ~ . T h e r e d o x p e a k is seen in b o t h i n - p h a s e a n d q u a d r a t u r e c o m p o n e n t s a r o u n d --o.28 V, a n d t h e n e g a t i v e faradaic a d m i t t a n c e is clearly visible, especially on t h e i n - p h a s e c o m p o n e n t (the few h i g h p o i n t s n e a r o.67 V on t h e q u a d r a t u r e c o m p o n e n t are d u e to a m o m e n t a r y oscillatory b e h a v i o r of t h e i n s t r u m e n t , w h i c h will occur w h e n a m e r c u r y droplet does n o t dislodge p r o p e r l y f r o m t h e capillary).
12 y...,...,. .............. 10
i(/JA)
::.................................................................
.,,........
$
%..
6
4
""..... ........................ ."" 2
I 0 0
0.1
I ,,,i 0.2
0.3
I
I
I
I
0.4
0.5
0.6
0.7
0.8
I
I
I
I
I
I
I
0.9
1.0
U.
I,?.
1.5
L4
b5
-E (V vs. internal A g / A g S C N )
Fig. 8. P o l a r o g r a m of t h e solution of Fig. 7, o b t a i n e d b y a p p l y i n g zero a l t e r n a t i n g v o l t a g e a n d c o n n e c t i n g t h e recorder Y i n p u t directly to t h e o u t p u t of a m p . 6 (Fig. I). C u r v e g i v e n here for reference, s h o w i n g t h e position of t h e w a v e (with m a x i m u m ) n e a r --o.3 V, a n d of t h e polarographic minimum• j. Eledtroanal.
C h e m . , 20 (I969) 181-193
188
R. DE LEVIE, A, A. HUSOVSKY
negligible. One would think that positive feedback might eliminate this restriction completely, but this is not yet quite the case. Positive feedback forces the circuit to live continuously in the shadow of oscillations, resulting from phase shifts at high frequencies in small stray capacitances (Such oscillations may not always be apparent from the recorder output, since the synchronous rectifier rejects them quite efficiently ;wehave found it very useful to monitor more or less continuously the output of the summing amplifier ( # IO in Fig. i) on a scope (Hewlett Packard 13o C) which is also used for occasional checks of square wave symmetry and of other signals in the instrument). In order to restrain the oscillations we must restrict either the upper frequency limit of the instrument or .." '.. .%
c
1o
•
f
. .................. .....
E © o
+~ Ld
y... ................... t
0.7
0.8
I
O.D 1.0 11.1- E (V vs. (NaCI) S C E )
112
1.3
~.4
I
1.5
Fig. 9. I n - p h a s e and q u a d r a t u r e c o m p o n e n t s of the electrode a d m i t t a n c e of o.i M Ni(C104)2 in 2.8 M LiC104 at p H 6.88; Ni(OH)2 r e m o v e d b y centrifuge. <ernating voltage: 318 Hz; io m V amplitude. Compensated resistance: 193 f2. The slow reduction of Ni 2+ near --0.95 V and the m u c h faster reduction of a small a m o u n t (about o.i raM) of polymeric nickel a r o u n d -- 1.28 V are m o s t easily seen on tile in-phase c o m p o n e n t . Note the negative faradaic capacitance a r o u n d --1.24 V.
Fig. IO. P o l a r o g r a m of the solution of Fig. 9, showing the absence of a distinguishable wave near -- 1.28 V. Figs. 9 and io also illustrate t h a t a " t o t a l l y irreversible" polarographic w a v e still gives rise to a small faradaic admittance, in accordance with MATSUDA'S calculations~.
j . Electroanal. Chem., 2o (1969) I 8 I - I 9 3
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
18 9
the maximum resistance which the instrument can correct for. The present instrument yields results within the limits of recorder precision and readability (about __o.5 % of full scale) in solutions of o.I M ionic strength up to at least 5oo Hz, and still performs quite reasonably in solutions of o.oi M ionic strength. In o.ooi M solutions, useful data have been obtained only with a larger feedback capacitor (io nF) across the potentiostat amplifier ( # 3 in Fig. I) with a consequent diminution of usable frequency range. This makes the instrument still practicable for measurements of double-layer capacitance or photo-current in such dilute solutions, but severely limits its usefulness for the study of electrode kinetics at low ionic strength. condensor lens
mercury
focusin~ lens
interference
arc lamp
refocusin9 lens
[
quartz cell with optically flat window
[
filter fast chopper
dine
I slow chopper
rr
pulses for recorder sampling and m e r c u r y drop detachment
I
r e f e r e n c e signal
for
synchronous rectifier
Fig. i i. T h e optical s e t - u p u s e d for t h e m e a s u r e m e n t of photo-effects. All optical e l e m e n t s are q u a r t z . T h e f a s t (I 5-1ooo Hz) c h o p p e r p r o v i d e s a reference signal for t h e s y n c h r o n o u s rectifier, t h e slow (o.I Hz) c h o p p e r r e g u l a t e s recorder s a m p l i n g a n d d r o p - t i m e via two nlicroswitches.
6£
5C
40
."
-i(nA)
..."
30 ....."Photo20
10
...,.. ........
............-'""'
......,
..................................... o ..... 0.5
cur Pent
... -.""
!. . . . . . . . 0.6
dclPk c u P P e n t
!........... 0.7
•...............................................................................................................
0.8
0.9 1.0 -E (V vs. SCE)
1.1
1.2
1.3
1.4
1.5
Fig. 12. P h o t o - c u r r e n t of 0. 5 M N a F s a t d . w i t h N~O, m e a s u r e d w i t h t h e s e t - u p of Fig. i i . W a v e l e n g t h : 366 rim, h M f - w i d t h IO n m . F r e q u e n c y of f a s t c h o p p e r : 15. 9 H z ; c o m p e n s a t e d resistance 14o ~ . T h e a b o v e d a t a fit a linear plot ~0 of (--i) 0.4 vs. - - E . j . Electroanal. Chem., 20 (1969) 181-193
I90
R. DE LEVIE, A. A. HUSOVSKY
The frequency limitation is not a fundamental one but rather is inherent to the present design. Nevertheless it appears that an approach like that of HAYES AND REILLEY ls, which corrects a posteriori for the iR drop, is more readily extended to significantly higher frequencies. On the other hand, such an approach is not feasible when the electrochemical signal is generated in the electrode rather than in the external circuit, as is the case with photo-emission of electrons. The proper amount of positive feedback is found 14 by monitoring the in-phase component of the admittance in a region of potentials where no in-phase component should be present. Such a region can almost always be found. First, the required instrument sensitivity is selected and the instrument is phased (Fig. x, amplifier I2) using a series resistor-capacitor combination as d u m m y cell and the appropriate, calculated compensation for the series resistance. Proper phasing is achieved when the in-phase component vanishes from the output. The same procedure is then repeated with the cell, this time adjusting only the amount of positive feedback while leaving the sensitivity and phase controls untouched. In order to set the second pair of phase controls orthogonal to the first, the d u m m y cell capacitor is replaced b y a resistor, and the phase control potentiometer adjusted until the quadrature component in the output vanishes (on m a n y commercial lock-in amplifiers which might be substituted for amplifiers 7-I4, a 9o°-phase shift can easily be obtained b y turning a switch). Since the uncompensated solution resistance depends on tile size of the mercury drop, proper correction can only be achieved at one moment in drop life. The solution resistance decreases with time, so that overcompensation will occur after the selected balancing time, making the circuit more prone to oscillations. Therefore, the balancing point must be taken just before the drop falls, i.e., when the solution resistance is smallest and varies least. Only the reading taken at that moment is properly corrected for uncompensated resistance, and this is why the present instrument presents one data point per drop. Averaging of the signal over di'op life 19 amounts to only partial correction of uncompensated resistance. The uncompensated resistance is treated here as a function of drop size only, although, strictly speaking, it also depends on the electrode admittance. This is a consequence of the shielding effect of the bottom end of the capillary, which results in an uneven current distribution. As long as Yel is small, one has the secondary current distribution around the drop. The dimensionless parameter involved appears to be prYel where p is the solution resistivity (in ~ cm), r the drop radius (in cm) and Y~I the specific electrode admittance (in ~)-1 cm-O,). A secondary current distribution around the mercury drop can be anticipated* whenever prYe~ < I. Since p is of the order of IO/m ~ cm where m is the ionic strength in moles/l, and r is of the order of o.x cm near the end of the drop life, Yel should be much smaller than m f~ i cm-~ in order that the solution resistance be constant, and this is usually the case. For lowfrequency double-layer capacitance measurements this condition is certainly satisfied, but at high frequencies it m a y not be, as the following estimate shows: C = 2o#F cm -2 and 0)=500 sec -1 (about 80 Hz), or 500000 see -1 (about 80 kHz) yields Yel= IO -2 f1-1 cm -°~ or I ~ - 1 cm-~o, respectively. * See also the model experiments by GARDNER31. Apparently, the values of the dimensionless p a r a m e t e r , ~, given there are too large by a factor of lO 6, I n these experiments, the c u r r e n t density at the b o t t o m of the model electrode exceeds t h a t calculated by MATYg-g26, p r e s u m a b l y as a result of the close p r o x i m i t y of the auxiliary electrode.
j . Electroanal. Chem., 20 (1969) 181-193
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
191
In the complete absence of shielding, the solution resistance around a mercury drop 2~ is ~/4~r ~ cm 2, whereas the m a x i m u m effect of shielding (viz., the case of a primary current distribution, erYe 1>>I) corresponds 26,27 to an increase in resistance by a factor of 1.455. Consequently, the dependence of solution resistance on electrode admittance is small anyway, and has never been observed directly with capacitance measurements. The effect might become important whenever the faradaic admittance exceeds the double-layer capacitance b y m a n y orders of magnitude. The same holds for the similar effect resulting from uneven mass transport28, 29. Negative feedback enhances noise quite significantly, so that frequency-selective detectors are called for if low signal levels are required. Fortunately, phase-selective detectors are automatically frequency-selective. In a synchronous rectifier like the one used here, even harmonics do not contribute to the output, and ( 2 n + I ) t h harmonics are attenuated b y a factor (2n + I) when both switches are conducting for exactly half of the period of the fundamental frequency. If the square wave driving the F E T switches is asymmetrical, then harmonics are attenuated by a factor I i - ( - i ) n c o s n ~ l / n where ~ is the a s y m m e t r y of the square wave in radians (i.e., periods of ~ + ~ and ~ - ~ rather than two equal half-periods of ~ radians). Using scale expansion to avoid the first part of the sweep which is often not quite linear, a s y m m e t r y of 0.o 4 radians in the square wave driving the F E T s is readily detected on a monitoring scope. Such a s y m m e t r y would correspond to an error of o.4~o in the signal at the fundamental frequency, whereas any second harmonic is still attenuated more than 60 times. Hence, no significant amount of second harmonic ends up in the output, and the response at the fundamental frequency is not measurably affected, when the square wave is adjusted visually for correct s y m m e t r y with the potentiometer in the wave-squaring circuit, Fig. 2. As the amounts of nth harmonics resulting from non-linearities in the admittance-voltage relation are proportional to the nth power of the amplitude, the contributions of third, fifth etc., harmonics are usually negligible at excitation levels of Io-mV amplitude or less. In most commercial lock-in amplifiers, the signal first passes a narrow band pass filter in order to reject odd harmonics and to decrease the possibility of amplifier overload. However, very good frequency stability is required of both the oscillator and the filter lest phase shifts are introduced. Moreover, some sharply tuned filters tend to generate slowly decaying oscillations at their resonant frequency upon sudden variations in signal level as occur at drop fall, and these m a y still contribute measurably to the output at the end of the next drop life. The present instrument does not have, nor require, any such tuned filtering, and a change in operating frequency is achieved simply b y changing the oscillator frequency. Complete correction for uncompensated resistance m a y not always be feasible, as it m a y lead to oscillations. The error resulting from incomplete correction can readily be estimated from the recorded data. For a purely capacitive electrode admittance, the relative error in the measured capacitance is simply (y,/y,,)2 where Y' and Y " are the measured in-phase and quadrature components. Thus, if Y ' / Y " =0.05, the relative error in the measured capacitance is only 0.003, and even when Y' is IO~o of Y " , the resulting error in Y " is only I % . Thus, the error in Y " is almost always negligible, and moreover there is a clear warning whenever the instrumental compensation is inadequate, by the appearance of a non-zero in-phase
j. Electroanal. Chem., 20 (1969) 181-193
I92
R. DE LEVIE, A. A. HUSOVSKY
component in a region of potentials where it should not be present. If necessary, the resulting error in Y " can be corrected by calculation via Yeorr"=r"{r+(Y'/W")2}
The remaining, still uncompensated part of the resistance can be estimated from y,/{(y,)o+ (y,,)2} and might be used to check the reliability of data in the region where the electrode admittance is not purely capacitive. In general, a posteriori correction of data has not been found necessary unless the solutions are very dilute (less than o.oI M ionic strength). Strictly speaking, the present instrument records components of current rather than an admittance, i.e., the recorder response is directly proportional to tile amplitude of the alternating voltage. Division by the latter amplitude no doubt could have been accomplished by slightly modifying the recorder 15 but this does not seem to serve much purpose since the amplitude of the oscillator output is as stable as the amplifiers used in signal handling in the instrument. The present instrument provides data automatically, with the accuracy, speed, and convenience of a polarogram. The usefulness of the obtainable information can be judged from the illustrations given. The available frequency range is almost three orders of magnitude smaller than that of the best bridges, so that the instrument has only limited applicability to investigations of very fast electrode kinetics. However, for many measurements the instrument is quite adequate, and there its speed and reliability are very helpful features. ACKNOWLEDGEMENTS
Dr. L. P. ]V[ORGENTHALERand Mr. W. H. CRAIGgave valuable assistance in the design and construction of electronic circuits. The application to photo-emission of electrons was worked out in cooperation with Miss J. C. KREUSER and Mr. P. A. FENTON. Figures 9 and IO were taken from the yet unpublished work of B. KENNEDY AND L. t ). ~V[ORGENTHALERon the hydrolysis products of nickel. The present research was supported in part by the National Science Foundation under Grant GP 5432 and by the Air Force Office of Scientific Research, Office of Airospace Research, United States Air Force, under AFOSR grant 68-1344. SUMMARY
An instrument is described which will automatically plot the in-phase and quadrature components of the electrode admittance in the fashion of a polarogram. Correction for uncompensated series resistance is achieved by positive feedback, and synchronous rectification is used for signal detection. The limitations of the instrument are discussed, and illustrations of its applicability are given. REFERENCES I 2 3 4
G. LIPPMANIg, Compt. Rend., 76 (1873) 14o7; Pogg. Ann., 149 (1873) 561 ; J. Phys., 3 (1874) 41. G. GouY, Ann. Chim. Phys., 29 (19o3) 145. M. PROSKURNIN A~ID A. N. FRUMKIN, Trans. Faraday Sot.. ~I (1935) 11o. D. C. GRAHAME, J. Am. Chem. Soc., 63 (1941) 12o7.
J. Electroanal. Chem., 2o (1969) 181-193
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
193
5 D. C. GRAIIAMIg, Chem. Rev., 41 (1947) 441. 6 J. E. B. t{ANDLES, Discussions Faraday Sot., I (1947) 11,47; H. MATSUDA, Z. Elektrochem., 62 (1958 ) 977. 7 V. 1. MELIK GAIKAZYAN, Zh. Fiz. Khim., 26 (1952) 560. 8 P. DELAHAY, J. Phys. Chem., 7 ° (1966) 2069, 2373. 9 C. MACALEAVY, Belgian patent 443,oo3 (1941) ; French patent 886,848 (1942). IO B. PREYER AND V. GUTMANN, Trans. Faraday Soc., 42 (1946) 645,650; 43 (1947) 785, Discussions Faraday Soc., I (1947) 19. II G. JEssoP, British patent 64o,768 (195o). 12 G. JEssoP, British patent 776,543 (1957). 13 U n i v e c t o r P o l a r o g r a p h U n i t , C a m b r i d g e I n s t r u m e n t C o m p a n y , L t d . , L o n d o n . 14 E. R. BROWN, T. G. McCORD, D. E. SMITH AND D. D. DEFORD, Anal. Chem., 38 (1966) 1119. 15 S. W. HAYES AND C. N. RI~ILLEY, Anal. Chem., 37 (1965) I32~'. 16 W. JACKSON AND P. J. tLLVlNG, Anal. Chem., 28 (1956) 378; C. F. MORRISON, Generalized Instrumentation for Research and Teaching, W a s h i n g t o n S t a t e U n i v e r s i t y Press, P u l l m a n (Wash.), 1964, p. 96; D. POULI, J. R. HUFF AND J. C. PEARSON, Anal. Chem., 38 (1966) 382; G. LAUER AND R. 2~k. OSTERYOUN'G, Anal. Chem., 38 (1966) 11o6. 17 J. SCHGn, W. MEHL AND H. GERISCHER, Z. Elektrochem., 59 (1955) 144; Z. I{OWALSKI AND J. SRZEDNICKI, J. Electroanal. Chem., 8 (1964) 399. 18 M. T. KELLEY AND D. J. FISHER, Anal. Chem., 28 (1956) 113o. 19 IR. F. t~VILIA AND A. J. DI~FESrDERFER, Anal. Chem., 39 (1967) 188520 D. C. GRAHAME, Techn. Rept. to U.S.Office of Naval Research, I (March 9, 195o); 7 (Dec, 13, I95I). 21 A. •. FRUMKII'¢ AND V. I. MELIK GAIKAZYAN, Dokl. Akad. Nauk SSSR, 77 (1951) 85522 H. SHIRAI, J. Chem. Soc. Japan, Pure Chem. Sect., 81 (196o) 1248. 23 N. TANAKA, T. TAKEUCHI AND R. TAMAMUSHI, Bull. Chem. Soc. Japan, 37 (1964) 1435. 24 M. SLUYTERS-REHBACH, B. TIMMER AND J. H. SLUYTERS, Z . Physik. Chem. Frankfurt, 52 (1967) I. 25 D. ILKOVlG, Collection Czech. Chem. Commun., 4 (1932) 480. 26 Z. M A T ¥ ~ , Vdstn. Kralov. Ceske Spolecnosti Nauk, T#ida Mat. P#irod., 3 ° (1944) i. 27 I. M. KOLTHOFF, J. C. MARSHALL AND S. g . GUPTA, J. Electroanal. Chem., 3 (1962) 209. 28 H. MATSUDA, Bull. Chem. Soc. Japan, 26 (1953) 342. 29 R. DE LEVlE, J. Electroanal. Chem., 9 (1965) 311. 3 ° Yu.YA.GUREVICH, A. M. BRODSKII AND V. G. LEVlCH, Elektrokhim., 3 (1967) 13°2. 31 A. W. GARDNER, Polarography I964, edited b y G. J. HILLS, MacMillan, L o n d o n , 1966, p. 187.
j . Electroanal. Chem,, 20 (1969) 181-193
181
I N S T R U M E N T FOR T H E AUTOMATIC MEASUREMENT OF T H E E L E C T R O D E ADMITTANCE*
R. D E L E V I E AND A. A. H U S O V S K Y
Department of Chemistry, Georgetown University, Washington, D. C. 2ooo7 (U.S.A.) (Received A u g u s t 8th, 1968)
INTRODUCTION
The measurement of the electrode admittance is fundamental to modern electrochemistry. On the basis of the Lippmann equation 1, GouY 2 accurately predicted the double-layer capacitance of aqueous solutions like o. 5 M Na~S04 and o.5 M H2S04 from surface tension measurements of unparalleled precision. The direct measurement of the electrode admittance became possible only after PROSKURNIN AND FRUMKIN3 had demonstrated the effect of organic impurities on the capacitance of stationary electrodes, and after GRAHAME4 had developed instrumentation to circumvent this problem b y using a dropping mercury electrode. Since then, bridge measurements of the electrode admittance have been used extensively, and have contributed significantly to our understanding of the double-layer structure 5, the kinetics of electrode reactions 6 and adsorption processes 7, and, recently, of the interplay between adsorption and electrode kinetics s. All these developments were based on bridge measurements like those of GRAHAME a, which are precise but time-eonsmning. Many attempts have been made to obtain the same information more rapidly. So-called a.c. polarography was developed b y MACALEAVY9 and BREYER AND GUTMANN 10, but it neglected the effects of resistance in series with the electrode and the phase relationship between voltage and current. Modern instrumentation goes back to two patents of JESSOP, who introduced phase-sensitive detection 11 and automatic compensation for series resistance v i a positive feedback 12. An instrument incorporating these innovations 13 has found a rather limited acceptance for general electrochemical work as it was designed primarily for analytical use. Only recently have JESSOP'S ideas been incorporated in other instruments. DEFORD et al. 14 described an instrument which monitors the absolute magnitude and the in-phase component of the electrode admittance, using both positive feedback and phase-sensitive rectification. A different approach is that of HAYES AND R E I L L E Y 15, who described an instrument which elegantly avoids the difficulties of positive feedback and uses a multiplier for phaseselective detector. In the present communication, we will describe an instrument similar to that of DEFORD et al. 14 with the incorporation of modern lock-in techniques. This instrument has been in continuous use for well over a year without major * T h i s m a n u s c r i p t is s u b m i t t e d for p u b l i c a t i o n w i t h t h e u n d e r s t a n d i n g t h a t t h e U n i t e d S t a t e s G o v e r n m e n t is a u t h o r i z e d to r e p r o d u c e a n d d i s t r i b u t e r e p r i n t s for g o v e r n m e n t a l p u r p o s e s .
j . Electroanal. Chem., 20 (1969) 181-193
182
R. DE LEVlE, A. A. HUSOVSKY
breakdown, and has been applied to a number of problems ranging from measurements of double-layer capacitance and faradaic impedance to those of photo-emission of electrons. It is specifically designed for use with a dropping mercury electrode. CIRCUIT DESCRIPTION
An alternating voltage is derived via follower i and a divider network from an external oscillator, and is fed to the summing point (negative input) of a potentiostatbooster combination, 3 + 4, see Fig. I. Also fed to that summing point are an initial potential derived from the power supply via a potentiometer, a voltage ramp from integrator 2, the output of follower 5 sensing the potential of a reference electrode (the usual negative feedback loop) and a fraction of the output of current amplifier, 6. The latter signal provides the positive feedbackS2,14,16 correcting for resistance between the reference electrode and the negative input of amplifier 6. The output of amplifier 6 is passed through a second order high-pass filter 7, further amplified (8) and inverted (9)- The outputs of 8 and 9 are chopped by FET series switches, summed by amplifier IO and finally averaged by a third-order low-pass Butterworth filter i i . The signal driving the FET choppers is derived from the a.c. input after phase-shifting (i2), squaring, proportioning (13) and inverting (14). Thus,
INITIAL
OJ-EO0 SENSITIVWY OSCILLATOR IN ~"
AC AMPLITUDE
GAIN IO-IOOO
POSITIVE FEEDBACK
IOO
reference HIGH PASS FILTER
-isv ~ 5
O.I nF
zoo:.>
-
v leo
,'~1-I J t nF-I/,LF
/-/m
2c
LOW PASS FILTER
WAVE SQUARER
PHASE SHIFTER
Fig. i. The electronic circuit used. Amplifiers i - 6 control the voltage, ~nd ~mp. 7 - I 4 m e a s u r e t h e c u r r e n t via s y n c h r o n o u s rectification. Amp. 2: Philbrick SP 2 A U ; amp, 4: B u r r B r o w n 3oi6/25; a m p . 6: Philbrick P 45 AU; all other a m p . : Philbrick P 65 A H U . Resistors: Sprague metal film t y p e 420 EBC 3, values in k ~ (except for I G~2 in r a m p generator circuit); t r a n s i s t o r s : M P F lO 5. Resistor box in positive feedback loop: General Radio 1434 G. The c o m p e n s a t e d resistance is given b y R R ' / I O ( R + 5 ) for R 4 1 o o , where R" is the value of the feedback resistor across amp. 6 (sensitivity) and R the value dialed on the positive feedback resistor box, all values t a k e n in k ~ . Only one of two identical phase-shifting RC n e t w o r k s is s h o w n on the positive i n p u t of a m p . I 2 ,
J. EIectroanal. Cl~em., 20 (1969) 181-193
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
183
amplifiers 7-I4 comprise a simple lock-in amplifier~t, 17 and may be replaced by a commercial unit. The following switches were omitted from Fig. I for greater clarity: a resethold-scan switch on the ramp generator 2, a switch connecting the positive input of follower 5 directly to the output of booster 4 (for use with 2 electrodes and dummy cells), a switch replacing the cell by a d u m m y consisting of a resistor in series with either .~G. PASS F,LTER 0__~.1
4
0.1
0.1
Low PASS F,-TEF~
4
0.[
200
400 ZOO 400 400
4-15V 20
5.6
5.6 1.5
IN ~
OUT
I 15
2N 4123
WAVE SQUARER
Fig. 2. T h e (second-order) h i g h - p a s s filter, (third-order) low-pass filter a n d w a v e - s q u a r e r of Fig. I. Amplifiers: P h i l b r i c k P 65 A H U . R e s i s t a n c e in kf2, c a p a c i t a n c e in # F . H5 VO¢
-15V
IN 2 0 7 t 6
54 A C .
865C
'41
)
2N 525
30tzg
2
1,651
/ **.sv 5,1
62<~
T-,sv 680pF 680 pE 5.1
4.7IF
ALLIED
120
~¢ISV
Fig. 3. Circuit d r i v i n g t h e h a m m e r coil (Guardian) a n d a double-pole d o u b l e - t h r o w r e l a y (Allied) w h i c h switches one p h a s e - s h i f t i n g R C c o m b i n a t i o n on a m p . 12 for a n o t h e r , t h u s yielding altern a t e l y i n - p h a s e a n d q u a d r a t u r e readings. C o n n e c t i n g p o i n t a or b to g r o u n d via 22 k ~ will fix t h e position of t h e r e l a y so t h a t o n l y one v e c t o r c o m p o n e n t is registered, as in Fig. 4. R e s i s t a n c e in kf~.
j . Electroanal. Chem., 2o[(1969) 181-193
I84
R. DE LEVIE, A. A. HUSOVSKY
another resistor or a capacitor (for phase adjustment and calibration), and finally a relay-driven switch replacing one adjustable resistor-capacitor combination by another, similar one in the phase-shifting network of amplifier 12. Details of the filters and of the wave squarer (a simple Schmidt trigger) are given in Fig. 2. The potentiometers for initial potential and ramp speed can be connected to + I5V , ground, or - I 5 V on the Philbrick PR3oo power supply used. Separate + I5V and - I 5 V wires lead from the power supply to each amplifier. Right at the amplifier sockets, I5-/,F electrolytic capacitors are connected between ground and the power supply terminals in order to prevent high-frequency signal transmission via the power supply. The ground bus is made out of 1/8 in. o.d. copper tubing, with connections kept as short as possible. Oscillator used: General Radio I3IoA; XY recorder: Hewiett Packard 7035 BM. Figure 3 illustrates the switching mechanism which regulates the drop-time. A synchronous motor drives a cam which actuates two microswitches, MI and M2. Closing of MI deactivates the electrical pen lift on the recorder, so that a data point is plotted. Closing of ~ 2 drives a hammer which dislodges a mercury droplet f ore the electrode, and also replaces one phase-shifting network (Fig. I, amplifier 12) by the other. Thus, alternate readings can yield the in-phase and quadrature components of the electrode admittance. A manual switch-setting overrides the alternation of phase-shifting networks in case only one component is wanted. INSTRUMENT PERFORMANCE
Measurements on a dummy cell (o.I-I/~F in series with o . i - i o o k~) indicated that adequate correction for uncompensated resistance up to about io k ~ can be achieved at frequencies up to about i kHz. At higher frequencies, phase shifts in the feedback loop prevent proper compensation. Reduction of the feedback capacitor across the potentiostat amplifier (3 in Fig. I) raises the frequency limit, but invariably leads to uncontrollable oscillations when the dummy is replaced by an actual electrochemical cell. Other feedback configurations 16 and other amplifiers have been tried, but the performance seems to be roughly the same. Apparently, stray capacitance and inductance in tile instrument, the cell and the cell leads, limits the frequency response. The lower frequency limit of the instrument is determined by the Butterworth filters used, The filters of Fig. 2 have 3 db. points of about 16 Hz. Operation at somewhat lower frequencies using other filters, is quite feasible as long as the frequency used significantly exceeds those associated with drop growth is and as long as the low-pass output filter does not introduce a measurable time-lag which would lead to a ~'esponse which is too low, especially when the instrument is calibrated with a dummy cell. This latter point is not always appreciated 19, A fair idea of the performance of the instrument can be obtained from the following examples. Figure 4 shows actual measurements (every single mercury droplet yields one single point) of the double-layer capacitance of o.I M KC1 at 200 Hz. Comparison with data obtained by GRA!4AME ~°, Fig. 5, shows agreement to within the readability of tile recorder data. Figure 6 shows the in-phase and quadrature components of the electrode impedance of a solution of hexamethylphosphoramide. Note that the desad* peaks exhibit both in-phase and quadrature components at this * desorption-adsorption
j . Electroanal. Chem., 20 (1969) 181-193
I85
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
h
0.8
-..
3
8
~ 0.6
.+2_
E ~ 0.4
2 El
I
0,2
02
I
0.4
£~.6 0.8 -E(V vs. intePnal Ag/AgCI)
I
1!0
1.2
Fig. 4. Q u a d r a t u r e c o m p o n e n t of the electrode a d m i t t a n c e for o. i M KC1 at 25 o. Alternating voltage : 2o0 Hz, amplitude io m V (20 mV top-to-top). Compensated resistance: 322~. E v e r y single p o i n t corresponds to one m e r c u r y droplet. D r o p - t i m e regulated at 6.o0 sec. B o t t o m curve shifted b y o,8 V, covering range, - - i . o to --1.8 V. An independent, duplicate r u n does n o t differ b y more t h a n o. 5 m m in a d m i t t a n c e over the whole range of potentials; o. 5 m m corresponds to o. 15 # F cm-2. This suggests t h a t the m a i n source of error is the readability of the recorder trace. A digital voltmeter, gated b y the pen-lowering signal, m i g h t be used to c i r c u m v e n t this difficulty if higher readability is required. I n s t r u m e n t sensitivity w a s calibrated w i t h capacitors of accurately k n o w n capacitance, hence the a d m i t t a n c e axis is indicated in t e r m s of microfarads. The p r o p e r u n i t of admittance, ~ t, is obtained b y multiplication of the capacitance, in farads, b y the a n g u l a r frequency ~o of the sine w a v e used. This explains the use of, e.g., 318 Hz (o~ ~ 2000 t a d sec -1) in Fig. 6. 4O
30
~7 v
2O
~s
1 0.2
I o,4
I
I 0.6
I
I o.e
I
t
I
I,o
-E(Vvs. Tnterna/ Ag/Ag Cl)
Fig. 5. Comparison of double-layer capacitance d a t a calcd, from Fig. 4 (points) and bridge m e a s u r e m e n t s of GRAHAME20 (line). Note the e x p a n d e d capacitance scale. F o r the calculation, the following measured d a t a were used: m e r c u r y mass flow rate 0.635--0.007 mg sec 1, drop age 5.867±O.OLO sec, corresponding to a spherical drop of 2.045 ~ o . o I 5 ram2 surface area. The potential scale used is 37 m V negative with respect to o.i NCE, 16 m V more positive t h a n NCE.
j . Electroanal. Chem., 20 (1969) 181-193
186
R. DE LEVIE, A. A. HUSOVSKY
frequency, in agreement with theory ~1. Figure 7 illustrates the redox* peak of indium(III) in thiocyanate, and the negative Faradaic admittance22, 23 in the region of the polarographic minimum, Fig. 8. Bridge measurements in the latter region are often hampered by oscillations 24 resulting from the interplay of tile negative admittance and the inductance of bridge transformers. Figure 9 shows the highly irreversible reduction of hexaquonickel(II) and the more reversible reduction of a basic nickel polymer. The latter is not obvious from the d.c. polarogram (Fig. Io) in view of its
°'7t .." 0.6
."'
-
::
•
~o.41 ~
. '.
O.
"
-~ o.2~ 0.1
"
: ..
0
"-
0.2
" . . . . . . . . . . .
.=
........~....................J..................!...................!...................~..; ,,....!................!....._......~ 0,4
0.6
0.8
1.0
L2
1.4
1.6
1-8
- E ( V VS. S C E )
Fig. 6. Q u a d r a t u r e (top) and in-phase (bottom) c o m p o n e n t s of the electrode a d m i t t a n c e of o.I M N a F satd. w i t h N20 a n d containing o.1% (v]v) of h e x a m e t h y l p h o s p h o r a m i d e , OP(N(CH3)2)a. Alternating voltage: 318 Hz, amplitude io inV. Compensated resistance: 616 ~ . Note the inp h a s e c o m p o n e n t s of the desad peaks,
low concentration (about o.1% of the total nickel concentration). Finally, Fig. i i shows how this type of instrumentation can be used to measure electrochemical photocurrents. In this case, the wave generator is omitted, and the mercury drop illuminated with monochromatic light, obtained in our set-up from a Ioo-W mercury lamp (PEK IiO) with quartz collimator lense, interference filter, two choppers and focusing lenses. One chopper interrupts the light beam at a frequency in the range, 15-Iooo Hz, with a separate photo-detector providing the reference signal for the synchronous rectification. The second chopper rotates at o. i Hz, alternately passing and interrupting the light beam for periods of 5 sec. It also actuates the microswitches regulating the pen lift and drop hammer. Consequently, alternate points indicate photo-current and dark current, see Fig. 12. The above data are presented for the purpose of illustration only. We will elaborate on the electrochemical aspects of some of the above systems in another publication. DISCUSSION
A.c. polarography without correction for uncompensated resistance is restricted to low frequencies, low solution resistivity and low concentrations of electroreducible substances, for the effects of uncompensated (solution and capillary) resistance to be * reduction-oxidation
f . Electroanal. Chem., 2o (1969) 181-193
z87
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
..." .."
0.5 i... ................................ ,-:
.:.'"-....
..
•
.
..
..
j
""....
electrode 0.4 - a d m i t t a n c e (~F)
.,
, .. j-":
O~
quadrature
0.2 ~
.
component
0,1 - -
..
,., ..:"
J..................................... .:' o
1
1
0.1
0. 9
I 0.3
I................. 1..... I 0.4 0.5 ",.0.6
I O~
I 0.8
I 0.9
-0.1
:, .-
-0.2
.:'1
.'" 1.0
I I.I
I 1.2
I 1.4
I 1.3
I 1.5
- E (V vs. internal Ag/AgSCN)
." in-phase : component
-0.3
-0~"
-0.5
"......
Fig. 7. I n - p h a s e a n d q u a d r a t u r e c o m p o n e n t s of t h e electrode a d m i t t a n c e of 2 m M In(SCN)3 in I.O M N a S C N acidified w i t h H S C N to p H 3.24 a t 25 °. A l t e r n a t i n g voltage: 31.8 Hz, a m p l i t u d e io mV. C o m p e n s a t e d resistance: 2o6 ~ . T h e r e d o x p e a k is seen in b o t h i n - p h a s e a n d q u a d r a t u r e c o m p o n e n t s a r o u n d --o.28 V, a n d t h e n e g a t i v e faradaic a d m i t t a n c e is clearly visible, especially on t h e i n - p h a s e c o m p o n e n t (the few h i g h p o i n t s n e a r o.67 V on t h e q u a d r a t u r e c o m p o n e n t are d u e to a m o m e n t a r y oscillatory b e h a v i o r of t h e i n s t r u m e n t , w h i c h will occur w h e n a m e r c u r y droplet does n o t dislodge p r o p e r l y f r o m t h e capillary).
12 y...,...,. .............. 10
i(/JA)
::.................................................................
.,,........
$
%..
6
4
""..... ........................ ."" 2
I 0 0
0.1
I ,,,i 0.2
0.3
I
I
I
I
0.4
0.5
0.6
0.7
0.8
I
I
I
I
I
I
I
0.9
1.0
U.
I,?.
1.5
L4
b5
-E (V vs. internal A g / A g S C N )
Fig. 8. P o l a r o g r a m of t h e solution of Fig. 7, o b t a i n e d b y a p p l y i n g zero a l t e r n a t i n g v o l t a g e a n d c o n n e c t i n g t h e recorder Y i n p u t directly to t h e o u t p u t of a m p . 6 (Fig. I). C u r v e g i v e n here for reference, s h o w i n g t h e position of t h e w a v e (with m a x i m u m ) n e a r --o.3 V, a n d of t h e polarographic minimum• j. Eledtroanal.
C h e m . , 20 (I969) 181-193
188
R. DE LEVIE, A, A. HUSOVSKY
negligible. One would think that positive feedback might eliminate this restriction completely, but this is not yet quite the case. Positive feedback forces the circuit to live continuously in the shadow of oscillations, resulting from phase shifts at high frequencies in small stray capacitances (Such oscillations may not always be apparent from the recorder output, since the synchronous rectifier rejects them quite efficiently ;wehave found it very useful to monitor more or less continuously the output of the summing amplifier ( # IO in Fig. i) on a scope (Hewlett Packard 13o C) which is also used for occasional checks of square wave symmetry and of other signals in the instrument). In order to restrain the oscillations we must restrict either the upper frequency limit of the instrument or .." '.. .%
c
1o
•
f
. .................. .....
E © o
+~ Ld
y... ................... t
0.7
0.8
I
O.D 1.0 11.1- E (V vs. (NaCI) S C E )
112
1.3
~.4
I
1.5
Fig. 9. I n - p h a s e and q u a d r a t u r e c o m p o n e n t s of the electrode a d m i t t a n c e of o.i M Ni(C104)2 in 2.8 M LiC104 at p H 6.88; Ni(OH)2 r e m o v e d b y centrifuge. <ernating voltage: 318 Hz; io m V amplitude. Compensated resistance: 193 f2. The slow reduction of Ni 2+ near --0.95 V and the m u c h faster reduction of a small a m o u n t (about o.i raM) of polymeric nickel a r o u n d -- 1.28 V are m o s t easily seen on tile in-phase c o m p o n e n t . Note the negative faradaic capacitance a r o u n d --1.24 V.
Fig. IO. P o l a r o g r a m of the solution of Fig. 9, showing the absence of a distinguishable wave near -- 1.28 V. Figs. 9 and io also illustrate t h a t a " t o t a l l y irreversible" polarographic w a v e still gives rise to a small faradaic admittance, in accordance with MATSUDA'S calculations~.
j . Electroanal. Chem., 2o (1969) I 8 I - I 9 3
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
18 9
the maximum resistance which the instrument can correct for. The present instrument yields results within the limits of recorder precision and readability (about __o.5 % of full scale) in solutions of o.I M ionic strength up to at least 5oo Hz, and still performs quite reasonably in solutions of o.oi M ionic strength. In o.ooi M solutions, useful data have been obtained only with a larger feedback capacitor (io nF) across the potentiostat amplifier ( # 3 in Fig. I) with a consequent diminution of usable frequency range. This makes the instrument still practicable for measurements of double-layer capacitance or photo-current in such dilute solutions, but severely limits its usefulness for the study of electrode kinetics at low ionic strength. condensor lens
mercury
focusin~ lens
interference
arc lamp
refocusin9 lens
[
quartz cell with optically flat window
[
filter fast chopper
dine
I slow chopper
rr
pulses for recorder sampling and m e r c u r y drop detachment
I
r e f e r e n c e signal
for
synchronous rectifier
Fig. i i. T h e optical s e t - u p u s e d for t h e m e a s u r e m e n t of photo-effects. All optical e l e m e n t s are q u a r t z . T h e f a s t (I 5-1ooo Hz) c h o p p e r p r o v i d e s a reference signal for t h e s y n c h r o n o u s rectifier, t h e slow (o.I Hz) c h o p p e r r e g u l a t e s recorder s a m p l i n g a n d d r o p - t i m e via two nlicroswitches.
6£
5C
40
."
-i(nA)
..."
30 ....."Photo20
10
...,.. ........
............-'""'
......,
..................................... o ..... 0.5
cur Pent
... -.""
!. . . . . . . . 0.6
dclPk c u P P e n t
!........... 0.7
•...............................................................................................................
0.8
0.9 1.0 -E (V vs. SCE)
1.1
1.2
1.3
1.4
1.5
Fig. 12. P h o t o - c u r r e n t of 0. 5 M N a F s a t d . w i t h N~O, m e a s u r e d w i t h t h e s e t - u p of Fig. i i . W a v e l e n g t h : 366 rim, h M f - w i d t h IO n m . F r e q u e n c y of f a s t c h o p p e r : 15. 9 H z ; c o m p e n s a t e d resistance 14o ~ . T h e a b o v e d a t a fit a linear plot ~0 of (--i) 0.4 vs. - - E . j . Electroanal. Chem., 20 (1969) 181-193
I90
R. DE LEVIE, A. A. HUSOVSKY
The frequency limitation is not a fundamental one but rather is inherent to the present design. Nevertheless it appears that an approach like that of HAYES AND REILLEY ls, which corrects a posteriori for the iR drop, is more readily extended to significantly higher frequencies. On the other hand, such an approach is not feasible when the electrochemical signal is generated in the electrode rather than in the external circuit, as is the case with photo-emission of electrons. The proper amount of positive feedback is found 14 by monitoring the in-phase component of the admittance in a region of potentials where no in-phase component should be present. Such a region can almost always be found. First, the required instrument sensitivity is selected and the instrument is phased (Fig. x, amplifier I2) using a series resistor-capacitor combination as d u m m y cell and the appropriate, calculated compensation for the series resistance. Proper phasing is achieved when the in-phase component vanishes from the output. The same procedure is then repeated with the cell, this time adjusting only the amount of positive feedback while leaving the sensitivity and phase controls untouched. In order to set the second pair of phase controls orthogonal to the first, the d u m m y cell capacitor is replaced b y a resistor, and the phase control potentiometer adjusted until the quadrature component in the output vanishes (on m a n y commercial lock-in amplifiers which might be substituted for amplifiers 7-I4, a 9o°-phase shift can easily be obtained b y turning a switch). Since the uncompensated solution resistance depends on tile size of the mercury drop, proper correction can only be achieved at one moment in drop life. The solution resistance decreases with time, so that overcompensation will occur after the selected balancing time, making the circuit more prone to oscillations. Therefore, the balancing point must be taken just before the drop falls, i.e., when the solution resistance is smallest and varies least. Only the reading taken at that moment is properly corrected for uncompensated resistance, and this is why the present instrument presents one data point per drop. Averaging of the signal over di'op life 19 amounts to only partial correction of uncompensated resistance. The uncompensated resistance is treated here as a function of drop size only, although, strictly speaking, it also depends on the electrode admittance. This is a consequence of the shielding effect of the bottom end of the capillary, which results in an uneven current distribution. As long as Yel is small, one has the secondary current distribution around the drop. The dimensionless parameter involved appears to be prYel where p is the solution resistivity (in ~ cm), r the drop radius (in cm) and Y~I the specific electrode admittance (in ~)-1 cm-O,). A secondary current distribution around the mercury drop can be anticipated* whenever prYe~ < I. Since p is of the order of IO/m ~ cm where m is the ionic strength in moles/l, and r is of the order of o.x cm near the end of the drop life, Yel should be much smaller than m f~ i cm-~ in order that the solution resistance be constant, and this is usually the case. For lowfrequency double-layer capacitance measurements this condition is certainly satisfied, but at high frequencies it m a y not be, as the following estimate shows: C = 2o#F cm -2 and 0)=500 sec -1 (about 80 Hz), or 500000 see -1 (about 80 kHz) yields Yel= IO -2 f1-1 cm -°~ or I ~ - 1 cm-~o, respectively. * See also the model experiments by GARDNER31. Apparently, the values of the dimensionless p a r a m e t e r , ~, given there are too large by a factor of lO 6, I n these experiments, the c u r r e n t density at the b o t t o m of the model electrode exceeds t h a t calculated by MATYg-g26, p r e s u m a b l y as a result of the close p r o x i m i t y of the auxiliary electrode.
j . Electroanal. Chem., 20 (1969) 181-193
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
191
In the complete absence of shielding, the solution resistance around a mercury drop 2~ is ~/4~r ~ cm 2, whereas the m a x i m u m effect of shielding (viz., the case of a primary current distribution, erYe 1>>I) corresponds 26,27 to an increase in resistance by a factor of 1.455. Consequently, the dependence of solution resistance on electrode admittance is small anyway, and has never been observed directly with capacitance measurements. The effect might become important whenever the faradaic admittance exceeds the double-layer capacitance b y m a n y orders of magnitude. The same holds for the similar effect resulting from uneven mass transport28, 29. Negative feedback enhances noise quite significantly, so that frequency-selective detectors are called for if low signal levels are required. Fortunately, phase-selective detectors are automatically frequency-selective. In a synchronous rectifier like the one used here, even harmonics do not contribute to the output, and ( 2 n + I ) t h harmonics are attenuated b y a factor (2n + I) when both switches are conducting for exactly half of the period of the fundamental frequency. If the square wave driving the F E T switches is asymmetrical, then harmonics are attenuated by a factor I i - ( - i ) n c o s n ~ l / n where ~ is the a s y m m e t r y of the square wave in radians (i.e., periods of ~ + ~ and ~ - ~ rather than two equal half-periods of ~ radians). Using scale expansion to avoid the first part of the sweep which is often not quite linear, a s y m m e t r y of 0.o 4 radians in the square wave driving the F E T s is readily detected on a monitoring scope. Such a s y m m e t r y would correspond to an error of o.4~o in the signal at the fundamental frequency, whereas any second harmonic is still attenuated more than 60 times. Hence, no significant amount of second harmonic ends up in the output, and the response at the fundamental frequency is not measurably affected, when the square wave is adjusted visually for correct s y m m e t r y with the potentiometer in the wave-squaring circuit, Fig. 2. As the amounts of nth harmonics resulting from non-linearities in the admittance-voltage relation are proportional to the nth power of the amplitude, the contributions of third, fifth etc., harmonics are usually negligible at excitation levels of Io-mV amplitude or less. In most commercial lock-in amplifiers, the signal first passes a narrow band pass filter in order to reject odd harmonics and to decrease the possibility of amplifier overload. However, very good frequency stability is required of both the oscillator and the filter lest phase shifts are introduced. Moreover, some sharply tuned filters tend to generate slowly decaying oscillations at their resonant frequency upon sudden variations in signal level as occur at drop fall, and these m a y still contribute measurably to the output at the end of the next drop life. The present instrument does not have, nor require, any such tuned filtering, and a change in operating frequency is achieved simply b y changing the oscillator frequency. Complete correction for uncompensated resistance m a y not always be feasible, as it m a y lead to oscillations. The error resulting from incomplete correction can readily be estimated from the recorded data. For a purely capacitive electrode admittance, the relative error in the measured capacitance is simply (y,/y,,)2 where Y' and Y " are the measured in-phase and quadrature components. Thus, if Y ' / Y " =0.05, the relative error in the measured capacitance is only 0.003, and even when Y' is IO~o of Y " , the resulting error in Y " is only I % . Thus, the error in Y " is almost always negligible, and moreover there is a clear warning whenever the instrumental compensation is inadequate, by the appearance of a non-zero in-phase
j. Electroanal. Chem., 20 (1969) 181-193
I92
R. DE LEVIE, A. A. HUSOVSKY
component in a region of potentials where it should not be present. If necessary, the resulting error in Y " can be corrected by calculation via Yeorr"=r"{r+(Y'/W")2}
The remaining, still uncompensated part of the resistance can be estimated from y,/{(y,)o+ (y,,)2} and might be used to check the reliability of data in the region where the electrode admittance is not purely capacitive. In general, a posteriori correction of data has not been found necessary unless the solutions are very dilute (less than o.oI M ionic strength). Strictly speaking, the present instrument records components of current rather than an admittance, i.e., the recorder response is directly proportional to tile amplitude of the alternating voltage. Division by the latter amplitude no doubt could have been accomplished by slightly modifying the recorder 15 but this does not seem to serve much purpose since the amplitude of the oscillator output is as stable as the amplifiers used in signal handling in the instrument. The present instrument provides data automatically, with the accuracy, speed, and convenience of a polarogram. The usefulness of the obtainable information can be judged from the illustrations given. The available frequency range is almost three orders of magnitude smaller than that of the best bridges, so that the instrument has only limited applicability to investigations of very fast electrode kinetics. However, for many measurements the instrument is quite adequate, and there its speed and reliability are very helpful features. ACKNOWLEDGEMENTS
Dr. L. P. ]V[ORGENTHALERand Mr. W. H. CRAIGgave valuable assistance in the design and construction of electronic circuits. The application to photo-emission of electrons was worked out in cooperation with Miss J. C. KREUSER and Mr. P. A. FENTON. Figures 9 and IO were taken from the yet unpublished work of B. KENNEDY AND L. t ). ~V[ORGENTHALERon the hydrolysis products of nickel. The present research was supported in part by the National Science Foundation under Grant GP 5432 and by the Air Force Office of Scientific Research, Office of Airospace Research, United States Air Force, under AFOSR grant 68-1344. SUMMARY
An instrument is described which will automatically plot the in-phase and quadrature components of the electrode admittance in the fashion of a polarogram. Correction for uncompensated series resistance is achieved by positive feedback, and synchronous rectification is used for signal detection. The limitations of the instrument are discussed, and illustrations of its applicability are given. REFERENCES I 2 3 4
G. LIPPMANIg, Compt. Rend., 76 (1873) 14o7; Pogg. Ann., 149 (1873) 561 ; J. Phys., 3 (1874) 41. G. GouY, Ann. Chim. Phys., 29 (19o3) 145. M. PROSKURNIN A~ID A. N. FRUMKIN, Trans. Faraday Sot.. ~I (1935) 11o. D. C. GRAHAME, J. Am. Chem. Soc., 63 (1941) 12o7.
J. Electroanal. Chem., 2o (1969) 181-193
AUTOMATIC MEASUREMENT OF ELECTRODE ADMITTANCE
193
5 D. C. GRAIIAMIg, Chem. Rev., 41 (1947) 441. 6 J. E. B. t{ANDLES, Discussions Faraday Sot., I (1947) 11,47; H. MATSUDA, Z. Elektrochem., 62 (1958 ) 977. 7 V. 1. MELIK GAIKAZYAN, Zh. Fiz. Khim., 26 (1952) 560. 8 P. DELAHAY, J. Phys. Chem., 7 ° (1966) 2069, 2373. 9 C. MACALEAVY, Belgian patent 443,oo3 (1941) ; French patent 886,848 (1942). IO B. PREYER AND V. GUTMANN, Trans. Faraday Soc., 42 (1946) 645,650; 43 (1947) 785, Discussions Faraday Soc., I (1947) 19. II G. JEssoP, British patent 64o,768 (195o). 12 G. JEssoP, British patent 776,543 (1957). 13 U n i v e c t o r P o l a r o g r a p h U n i t , C a m b r i d g e I n s t r u m e n t C o m p a n y , L t d . , L o n d o n . 14 E. R. BROWN, T. G. McCORD, D. E. SMITH AND D. D. DEFORD, Anal. Chem., 38 (1966) 1119. 15 S. W. HAYES AND C. N. RI~ILLEY, Anal. Chem., 37 (1965) I32~'. 16 W. JACKSON AND P. J. tLLVlNG, Anal. Chem., 28 (1956) 378; C. F. MORRISON, Generalized Instrumentation for Research and Teaching, W a s h i n g t o n S t a t e U n i v e r s i t y Press, P u l l m a n (Wash.), 1964, p. 96; D. POULI, J. R. HUFF AND J. C. PEARSON, Anal. Chem., 38 (1966) 382; G. LAUER AND R. 2~k. OSTERYOUN'G, Anal. Chem., 38 (1966) 11o6. 17 J. SCHGn, W. MEHL AND H. GERISCHER, Z. Elektrochem., 59 (1955) 144; Z. I{OWALSKI AND J. SRZEDNICKI, J. Electroanal. Chem., 8 (1964) 399. 18 M. T. KELLEY AND D. J. FISHER, Anal. Chem., 28 (1956) 113o. 19 IR. F. t~VILIA AND A. J. DI~FESrDERFER, Anal. Chem., 39 (1967) 188520 D. C. GRAHAME, Techn. Rept. to U.S.Office of Naval Research, I (March 9, 195o); 7 (Dec, 13, I95I). 21 A. •. FRUMKII'¢ AND V. I. MELIK GAIKAZYAN, Dokl. Akad. Nauk SSSR, 77 (1951) 85522 H. SHIRAI, J. Chem. Soc. Japan, Pure Chem. Sect., 81 (196o) 1248. 23 N. TANAKA, T. TAKEUCHI AND R. TAMAMUSHI, Bull. Chem. Soc. Japan, 37 (1964) 1435. 24 M. SLUYTERS-REHBACH, B. TIMMER AND J. H. SLUYTERS, Z . Physik. Chem. Frankfurt, 52 (1967) I. 25 D. ILKOVlG, Collection Czech. Chem. Commun., 4 (1932) 480. 26 Z. M A T ¥ ~ , Vdstn. Kralov. Ceske Spolecnosti Nauk, T#ida Mat. P#irod., 3 ° (1944) i. 27 I. M. KOLTHOFF, J. C. MARSHALL AND S. g . GUPTA, J. Electroanal. Chem., 3 (1962) 209. 28 H. MATSUDA, Bull. Chem. Soc. Japan, 26 (1953) 342. 29 R. DE LEVlE, J. Electroanal. Chem., 9 (1965) 311. 3 ° Yu.YA.GUREVICH, A. M. BRODSKII AND V. G. LEVlCH, Elektrokhim., 3 (1967) 13°2. 31 A. W. GARDNER, Polarography I964, edited b y G. J. HILLS, MacMillan, L o n d o n , 1966, p. 187.
j . Electroanal. Chem,, 20 (1969) 181-193